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Modelling non-additive and nonlinear signals from climatic noise in ecological time series: Soay sheep as an example.

ABSTRACT: Understanding how climate can interact with other factors in determining patterns of species abundance is a persistent challenge in ecology. Recent research has suggested that the dynamics exhibited by some populations may be a non-additive function of climate, with climate affecting population growth more strongly at high density than at low density. However, we lack methodologies to adequately explain patterns in population growth generated as a result of interactions between intrinsic factors and extrinsic climatic variation in non-linear systems. We present a novel method (the Functional Coefficient Threshold Auto-Regressive (FCTAR) method) that can identify interacting influences of climate and density on population dynamics from time-series data. We demonstrate its use on count data on the size of the Soay sheep population, which is known to exhibit dynamics generated by nonlinear and non-additive interactions between density and climate, living on Hirta in the St Kilda archipelago. The FCTAR method suggests that climate fluctuations can drive the Soay sheep population between different dynamical regimes--from stable population size through limit cycles and non-periodic fluctuations.

SUBMITTER: Stenseth NC

PROVIDER: S-EPMC1691829 | biostudies-literature | 2004 Oct

REPOSITORIES: biostudies-literature

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Modelling non-additive and nonlinear signals from climatic noise in ecological time series: Soay sheep as an example.

Stenseth Nils Chr NC Chan Kung-Sik KS Tavecchia Giacomo G Coulson Tim T Mysterud Atle A Clutton-Brock Tim T Grenfell Bryan B

Proceedings. Biological sciences 20041001 1552

Understanding how climate can interact with other factors in determining patterns of species abundance is a persistent challenge in ecology. Recent research has suggested that the dynamics exhibited by some populations may be a non-additive function of climate, with climate affecting population growth more strongly at high density than at low density. However, we lack methodologies to adequately explain patterns in population growth generated as a result of interactions between intrinsic factors ...[more]

PMID: 15451687

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Project description:BackgroundThe objective of this study was to introduce a genome-wide association study (GWAS) in conjunction with segregation analysis on monogenic categorical traits. Genotype probabilities calculated from phenotypes, mode of inheritance and pedigree information, are expressed as the expected allele count (EAC) (range 0 to 2), and are inherited additively, by definition, unlike the original phenotypes, which are non-additive and could be of incomplete penetrance. The EAC are regressed on the single nucleotide polymorphism (SNP) genotypes, similar to an additive GWAS. In this study, horn phenotypes in Merino sheep are used to illustrate the advantages of using the segregation GWAS, a trait believed to be monogenic, affected by dominance, sex-dependent expression and likely affected by incomplete penetrance. We also used simulation to investigate whether incomplete penetrance can cause prediction errors in Merino sheep for horn status.ResultsEstimated penetrance values differed between the sexes, where males showed almost complete penetrance, especially for horned and polled phenotypes, while females had low penetrance values for the horned status. This suggests that females homozygous for the 'horned allele' have a horned phenotype in only 22% of the cases while 78% will be knobbed or have scurs. The GWAS using EAC on 4001 animals and 510,174 SNP genotypes from the Illumina Ovine high-density (600k) chip gave a stronger association compared to using actual phenotypes. The correlation between the EAC and the allele count of the SNP with the highest -log10(p-value) was 0.73 in males and 0.67 in females. Simulations using penetrance values found by the segregation analyses resulted in higher correlations between the EAC and the causative mutation (0.95 for males and 0.89 for females, respectively), suggesting that the most predictive SNP is not in full LD with the causative mutation.ConclusionsOur results show clear differences in penetrance values between males and female Merino sheep for horn status. Segregation analysis for a trait with mutually exclusive phenotypes, non-additive inheritance, and/or incomplete penetrance can lead to considerably more power in a GWAS because the linearized genotype probabilities are additive and can accommodate incomplete penetrance. This method can be extended to any monogenic controlled categorical trait of which the phenotypes are mutually exclusive.

Project description:Increasingly, often ecologist collects data with nonlinear trends, heterogeneous variances, temporal correlation, and hierarchical structure. Nonlinear mixed-effects models offer a flexible approach to such data, but the estimation and interpretation of these models present challenges, partly associated with the lack of worked examples in the ecological literature.We illustrate the nonlinear mixed-effects modeling approach using temporal dynamics of vegetation moisture with field data from northwestern Patagonia. This is a Mediterranean-type climate region where modeling temporal changes in live fuel moisture content are conceptually relevant (ecological theory) and have practical implications (fire management). We used this approach to answer whether moisture dynamics varies among functional groups and aridity conditions, and compared it with other simpler statistical models. The modeling process is set out "step-by-step": We start translating the ideas about the system dynamics to a statistical model, which is made increasingly complex in order to include different sources of variability and correlation structures. We provide guidelines and R scripts (including a new self-starting function) that make data analyses reproducible. We also explain how to extract the parameter estimates from the R output.Our modeling approach suggests moisture dynamic to vary between grasses and shrubs, and between grasses facing different aridity conditions. Compared to more classical models, the nonlinear mixed-effects model showed greater goodness of fit and met statistical assumptions. While the mixed-effects approach accounts for spatial nesting, temporal dependence, and variance heterogeneity; the nonlinear function allowed to model the seasonal pattern.Parameters of the nonlinear mixed-effects model reflected relevant ecological processes. From an applied perspective, the model could forecast the time when fuel moisture becomes critical to fire occurrence. Due to the lack of worked examples for nonlinear mixed-effects models in the literature, our modeling approach could be useful to diverse ecologists dealing with complex data.

Dataset Information

Modelling non-additive and nonlinear signals from climatic noise in ecological time series: Soay sheep as an example.

Publications

Modelling non-additive and nonlinear signals from climatic noise in ecological time series: Soay sheep as an example.

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